Details

Time bar (total: 6.4s)

sample54.0ms

Algorithm
intervals
Results
35.0ms654×body80valid

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.0b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
9.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
54.0ms
(* (* a a) (+ 1.0 a))
121.0ms
(pow (+ (* a a) (* b b)) 2.0)
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify78.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
0564828
12826724
25001715

prune599.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
0.0b
(* (* (* b b) (- 1.0 (* 3.0 a))) 4.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log
18×add-cbrt-cube
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow-prod-down prod-exp cbrt-unprod
6×associate-*r* prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow
2×sub-neg flip3-- associate-*l* associate-*l/ *-commutative flip--
1×pow-to-exp pow-pow pow-exp fma-udef unswap-sqr sqr-pow
Counts
4 → 87
Calls
4 calls:
1.0ms
(fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
13.0ms
(* (* (* b b) (- 1.0 (* 3.0 a))) 4.0)
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
9.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
70.0ms
(* (* (* b b) (- 1.0 (* 3.0 a))) 4.0)
118.0ms
(pow (+ (* a a) (* b b)) 2.0)
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0447729
12112610
25002601

prune345.0ms

Filtered
99 candidates to 68 candidates (68.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
9.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series693.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
213.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
210.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
212.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04011582
116891442
250021408

prune451.0ms

Filtered
90 candidates to 74 candidates (82.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u flip3-+ pow1/3 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
7.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series805.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
201.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
190.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
201.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify133.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
02101764
17441632
237601572
350011560

prune488.0ms

Filtered
72 candidates to 72 candidates (100.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes153.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
12815

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20313×body80valid